Showing papers by "Uwe D. Hanebeck published in 2022"

Cryptographically Privileged State Estimation With Gaussian Keystreams

Abstract: State estimation via public channels requires additional planning with regards to state privacy and information leakage of involved parties. In some scenarios, it is desirable to allow partial leakage of state information, thus distinguishing between privileged and unprivileged estimators and their capabilities. Existing methods that make this distinction typically result in reduced estimation quality, require additional communication channels, or lack a formal cryptographic backing. We introduce a method to decrease estimation quality at an unprivileged estimator using a stream of pseudorandom Gaussian samples while leaving privileged estimation unaffected and requiring no additional transmission beyond an initial key exchange. First, a cryptographic definition of privileged estimation is given, capturing the difference between privileges, before a privileged estimation scheme meeting the security notion is presented. Achieving cryptographically privileged estimation without additional channel requirements allows quantifiable estimation to be made available to the public while keeping the best estimation private to trusted privileged parties and can find uses in a variety of service-providing and privacy-preserving scenarios.

Haptic Rendering of Arbitrary Serial Manipulators for Robot Programming

Abstract: The programming of manipulators is a common task in robotics, for which numerous solutions exist. In this work, a new programming method related to the common master-slave approach is introduced, in which the master is replaced by a digital twin created through haptic and visual rendering. To achieve this, we present an algorithm that enables the haptic rendering of any programmed robot with a serial manipulator on a general-purpose haptic interface. The results show that the proposed haptic rendering reproduces the kinematic properties of the programmed robot and directly provides the desired joint space trajectories. In addition to a stand-alone usage, we demonstrate that the proposed algorithm can be easily paired with existing visual technology for virtual and augmented reality to facilitate a highly immersive programming experience.

Asynchronous Multi-Radar Tracking Fusion with Converted Measurements

Abstract: In tracking applications, multiple radars used to observe target motion usually work asynchronously due to different sampling rates and initial sampling time instants, and the fusion time instant at the fusion center can be designated arbitrarily. In this paper, the estimation fusion problem for target tracking with asynchronous multi-rate multi-radar measurements is investigated. Two asynchronous fusion algorithms are proposed, i.e., batch time-aligned asynchronous fusion with unbiased converted measurements and sequential linear minimum mean square error (LMMSE) asynchronous fusion with converted measurements. The batch time-aligned asynchronous fusion algorithm is suboptimal because of the correlation between measurement error covariance and measurement itself. The sequential LMMSE asynchronous fusion algorithm is theoretically optimal in the sense of minimizing the mean square error within the set of all linear estimators. Numerical examples are provided to demonstrate the effectiveness of the proposed two asynchronous fusion algorithms.

Benchmarking a DEM‐CFD Model of an Optical Belt Sorter by Experimental Comparison

Abstract: A DEM-CFD (discrete element method - computational fluid dynamics) model of an optical belt sorter was extensively compared with experiments of a laboratory-scale sorter to assess the model’s accuracy. Brick and sand-lime brick were considered as materials. First, the transport characteristics on the conveyor belt, involving mass flow, lateral particle distribution and proximity, were compared. Second, sorting results were benchmarked for varying mixture proportions at differing mass flows. It was found that the numerical model is able to reproduce the experimental results with high accuracy. A DEM-CFD approach is used to model a full optical sorting system. By thorough comparison of characteristic quantities with experiments, the modelling capabilities of the approach are assessed. Non-spherical shaped particles of brick and sand-lime brick are used and represented as clustered spheres in the simulation.

Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization

Abstract: In this paper, we show how to analyze the achievable position accuracy of magnetic localization based on Bayesian Cramér-Rao lower bounds and how to account for deterministic inputs in the bound. The derivation of the bound requires an analytical model, e.g., a map or database, that links the position that is to be estimated to the corresponding magnetic field value. Unfortunately, finding an analytical model from the laws of physics is not feasible due to the complexity of the involved differential equations and the required knowledge about the environment. In this paper, we therefore use a Gaussian process (GP) that approximates the true analytical model based on training data. The GP ensures a smooth, differentiable likelihood and allows a strict Bayesian treatment of the estimation problem. Based on a novel set of measurements recorded in an indoor environment, the bound is evaluated for different sensor heights and is compared to the mean squared error of a particle filter. Furthermore, the bound is calculated for the case when only the magnetic magnitude is used for positioning and the case when the whole vector field is considered. For both cases, the resulting position bound is below 10cm indicating an high potential accuracy of magnetic localization.

Dirac Mixture Reduction Using Wasserstein Distances on Projected Cumulative Distributions

Abstract: The reapproximation of discrete probability densities is a common task in sample-based filters such as the particle filter. It can be viewed as the approximation of a given Dirac mixture density with another one, typically with fewer samples. In this paper, the Wasserstein distance is established as a suitable measure to compare two Dirac mixtures. The resulting minimization problem is also known as location-allocation or facility location problem and cannot be solved in polynomial time. Therefore, the well-known sliced Wasserstein distance is introduced as a replacement and its ties to the projected cumulative distribution (PCD) are shown. An iterative algorithm is proposed to minimize the sliced Wasserstein distance between the given distribution and approximation.

Circular Discrete Reapproximation

Abstract: We present a novel nonparametric scheme for modeling circular random variables. For that, the circular Cramer-von Mises distance (CCvMD) is proposed to measure the statistical divergence between two circular discrete models based on a smooth characterization of the localized cumulative distribution. Given a set of weighted samples from empirical data, the under-lying unknown distribution is then reapproximated by another sample set of configurable size and dispersion-adaptive layout in the sense of least CCvMD. Built upon the proposed circular discrete reapproximation (CDR), a new method is introduced for density estimation with von Mises mixtures. Moreover, the CDR scheme is extended to topological spaces composing the unit circle and Euclidean space of arbitrary dimension, and a new regression model for random circular vector fields is proposed based thereon. We provide case studies using synthetic and real-world data from wind climatology. Numerical results validate the efficacy of proposed approaches with promising potential of outperforming competitive methods.

Calibration-free IMU-based Kinematic State Estimation for Robotic Manipulators*

Abstract: The precise knowledge of a robot manipulator’s kinematic state including position, velocity, and acceleration is one of the base requirements for the application of advanced control algorithms. To obtain this information, encoder data could be differentiated numerically. However, the resulting velocity and acceleration estimates are either noisy or delayed as a result of low-pass filtering. Numerical differentiation can be circumvented by the utilization of gyroscopes and accelerometers, but these suffer from a variety of measurement errors and nonlinearity regarding the desired quantities. Therefore, we present a novel, real-time capable kinematic state estimator based on the Extended Kalman filter with states for the effective sensor biases. This way, the handling of arbitrary inertial sensor setups is made possible without calibration on manipulators composed of revolute and prismatic joints. Simulation experiments show that the proposed estimator is robust towards various error sources and that it outperforms competing approaches. Moreover, the practical relevance is demonstrated using a real manipulator with two joints.

Recursive Joint Cramér-Rao Lower Bound for Nonlinear Parametric Systems with Colored Noise

Abstract: The performance evaluation for joint state and parameter estimation (JSPE) is of great significance. Joint Cramér-Rao lower bound (JCRLB) has been widely studied for JSPE of nonlinear parametric systems with white noise. However, in practice, the noise is often colored due to high measurement frequency and bandlimited signal channels. In this paper, a recursive JCRLB is developed for JSPE of nonlinear parametric systems with colored noise, characterized by auto-regressive (AR) models. First, we propose a unified recursive JCRLB for JSPE of general nonlinear parametric systems with higher-order autocorrelated process noises and autocorrelated measurement noise simultaneously. Then its relationship with the posterior Cramér-Rao lower bound (PCRLB) for filtering of nonlinear systems with colored noise and the hybrid Cramér-Rao lower bound (HCRLB) for JSPE of regular parametric systems with white noise are provided. Illustrative examples in radar target tracking verify the effectiveness of the proposed JCRLB for the performance evaluation for JSPE of nonlinear parametric systems with colored noise.

Robot Joint Tracking With Mobile Depth Cameras for Augmented Reality Applications

Abstract: Augmented reality (AR) in mobile devices (such as smartphones and tablets) is becoming more popular each day, and because of this many newer devices are starting to ship with embedded depth sensors. This presents a great opportunity for the field of extended object tracking, whose algorithms are well-suited for dealing with varying measurement quality while requiring little CPU usage. In this paper, we present an application in the field of robotics, based on the idea of reconstructing the dynamic state of a robot (joint positions and velocities) simply by observing it with an AR device, and using only the robot specification (its URDF file) as prior knowledge, without requiring a connection to the robot's control system. This can allow the mobile device to identify where a robot is, or viceversa, without requiring markers such as QR codes. Additionally, this can serve as a stepping stone for more sophisticated assistance systems that can interact with the robot without requiring any access to its internals, which could otherwise make it difficult to deploy the AR app in sensitive systems. Using the iPad Pro 2020 as an example device, we examine the challenges involved in processing mobile depth images, how to develop a robust shape model and the corresponding estimator, and how the app can ask the user to help in its initialization using AR. We will also provide an evaluation with real data that shows how the proposed system can track a moving robot robustly even if measurement quality is reduced significantly.

Intuitive and immersive teleoperation of robot manipulators for remote decontamination

Abstract: Abstract Worker safety is one of the most important aspects of decontamination tasks in hazardous environments. This motivates the development of (semi-) autonomous robotic systems that can be teleoperated from a safe distance using simple commands such as ‘move the manipulator over there and grab’. In this paper, we introduce a new control station concept called Digital Twin Control System aimed at robots with manipulator arms. It consists of three components: (1) A unified communication interface that abstracts the remote robot’s functionalities into easy-to-use interaction modes, (2) an immersive visualization and assistant system to operate the interface, and (3) a haptic rendering system that can simulate arbitrary robot arms. We demonstrate how the proposed system can be used by untrained operators to pick up contaminated objects remotely in a test scenario.

Rejection Sampling from Arbitrary Multivariate Distributions Using Generalized Fibonacci Lattices

Abstract: We present a quasi-Monte Carlo acceptance-rejection sampling method for arbitrary multivariate continuous probability density functions. The method employs either a uni-form or a Gaussian proposal distribution. The proposal samples are provided by optimal deterministic sampling based on the generalized Fibonacci lattice. By using low-discrepancy samples from generalized Fibonacci lattices, we achieve a more locally homogeneous sample distribution than random sampling meth-ods for arbitrary continuous densities such as the Metropolis-Hastings algorithm or slice sampling, or acceptance-rejection based on state-of-the-art quasi-random sampling methods like the Sobol or Halton sequence.

The State Space Subdivision Filter for SE(3)

Abstract: Estimating the position and orientation of 3-D objects is a ubiquitous challenge. In our novel filter, the position and orientation of objects are modeled using the Cartesian product of ℝ for the position and a 3-D hyperhemisphere. The latter is used to describe orientations in the form of unit quaternions. The hyperhemisphere is subdivided into equally sized areas. The joint density for the position and orientation is split up into a marginal density for the orientation and a density for the position that is conditioned on the orientation. In our filter, we assume that the function values of the marginal density and the conditional density is the same for all points within that area. By assuming all conditional densities to be Gaussians, efficient formulae can be implemented for the update and prediction steps. The filter is evaluated based on a simulation scenario, for which it showed very high accuracy at low run times.

Optimal Sensor Placement for Multilateration Using Alternating Greedy Removal and Placement

Abstract: We present a novel algorithm for optimal sensor placement in multilateration problems. Our goal is to design a sensor network that achieves optimal localization accuracy anywhere in the covered region. We consider the discrete placement problem, where the possible locations of the sensors are selected from a discrete set. Thus, we obtain a combinatorial optimization problem instead of a continuous one. While at first, combinatorial optimization sounds like more effort, we present an algorithm that finds a globally optimal solution surprisingly quickly.

Event-Based Kalman Filtering Exploiting Correlated Trigger Information

Abstract: In networked estimation architectures, event-based sensing and communication can contribute to a more efficient resource allocation in general, and improved utilization of communication resources, in particular. In order to tap the full potential of event-based scheduling, the design of transmission triggers and estimators need to be closely coupled while two directions are promising: First, the remote estimator can exploit the absence of transmissions and translate it into implicit information about the sensor data. Second, an intelligent trigger mechanism at the sensor that predicts future sensor readings can decrease transmission rates while rendering the implicit information more valuable. Such an intelligent trigger has been developed in a recent paper based on a Finite Impulse Response filter, which requires the sensor to transmit an additional estimate alongside the measurement. In the present paper, the communication demand is further reduced by only transmitting the estimate. The remote estimator exploits correlations to incorporate the received information. In doing so, the estimation quality is also improved, which is confirmed by simulations.

Robust Particle Filter for Magnetic field-based Train Localization

Abstract: For the automation of railway systems, a crucial requirement is a reliable localization system that is able to localize all trains in the track network. While in most parts of the track network, GNSS signals are available and provide a satisfying navigation solution, there are also parts where shadowing and multipath renders GNSS signals unavailable. In such scenarios, magnetic field-based localization can complement GNSS. Magnetic field localization is based on the observation that ferromagnetic material in the vicinity of a railway track introduces distortions in the Earth magnetic field. These distortions are persistent over time and therefore can be used for localization when stored in a map. In our prior work we showed that particle filters can be used to perform magnetic localization. In this paper, we extend the particle filter with fault detection and exclusion capabilities to make it more robust and accurate in the presence of sensor faults and measurement errors. The advantage of the proposed particle filter w.r.t. accuracy and robustness is shown in an evaluation with measurement data.

Harmonic Functions for Three-Dimensional Shape Estimation in Cylindrical Coordinates

Abstract: With the high resolution of modern sensors such as multilayer LiDARs, estimating the 3D shape in an extended object tracking procedure is possible. In recent years, 3D shapes have been estimated in spherical coordinates using Gaussian processes, spherical double Fourier series or spherical harmonics. However, observations have shown that in many scenarios only a few measurements are obtained from top or bottom surfaces, leading to error-prone estimates in spherical coordinates. Therefore, in this paper we propose to estimate the shape in cylindrical coordinates instead, applying harmonic functions. Specifically, we derive an expansion for 3D shapes in cylindrical coordinates by solving a boundary value problem for the Laplace equation. This shape representation is then integrated in a plain greedy association model and compared to shape estimation procedures in spherical coordinates. Since the shape representation is only integrated in a basic estimator, the results are preliminary and a detailed discussion for future work is presented at the end of the paper.

Machine learning-based multiobject tracking for sensor-based sorting

Abstract: Sensor-based sorting provides state-of-the-art solutions for sorting of granular materials. Current systems use line-scanning sensors, which yields a single observation of each object only and no information about their movement. Recent works show that using an area-scan camera bears the potential to decrease both the error in characterization and separation. Using a multiobject tracking system, this enables an estimate of the followed paths as well as the parametrization of an individual motion model per object. While previous works focus on physically-motivated motion models, it has been shown that state-of-the-art machine learning methods achieve an increased prediction accuracy. In this paper, we present the development of a neural network-based multiobject tracking system and its integration into a laboratory-scale sorting system. Preliminary results show that the novel system achieves results comparable to a highly optimized Kalman filter-based one. A benefit lies in avoiding tiresome manual tuning of parameters of the motion model, as the novel approach allows learning its parameters by provided examples due to its data-driven nature.

Extent Estimation of Sailing Boats Applying Elliptic Cones to 3D LiDAR Data

Abstract: In this paper, approximating the shape of a sailing boat using elliptic cones is investigated. Measurements are assumed to be gathered from the target's surface recorded by 3D scanning devices such as multilayer LiDAR sensors. Therefore, different models for estimating the sailing boat's extent are presented and evaluated in simulated and real-world scenarios. In particular, the measurement source association problem is addressed in the models. Simulated investigations are conducted with a static and a moving elliptic cone. The real-world scenario was recorded with a Velodyne Alpha Prime (VLP-128) mounted on a ferry of Lake Constance. Final results of this paper constitute the extent estimation of a single sailing boat using LiDAR data applying various measurement models.